User blog:3primetime3/The Question of the Day - 2/13/2014
Hey guys! New users: even if an answer is already seen in the comments section, still write your answer. The answers not written by me still might not be right. For newcomers who are seeing this blog post for the first time, please read the rules to get started! ACHIEVEMENTS EARNED DURING THE LAST QUESTION: 0 The Question of the Day - ??? points There are 3 hard questions of the day. Get all three right to earn an achvmt pkg! Lucky Prime Hint! I am a 4-digit prime number that does not contain a 3. Question of the Day 1 (Calculators are permitted): Lilly orders a large, orange pineapple-flavored ice cream at the Ice Cream Shack. She immediately realizes that it would be too big for a cone, so she asks them to place it in a cup. Each scoop of ice cream is a perfect sphere with radius 3 inches (a specialty of the Shack). The cup the ice cream is placed in is a cylinder with diameter 7 inches and height 10 inches. If the scoops are gently placed in the cup, a large (3 scoops) would not fit in the cup, so the scoops are pressed into the cup so that all the ice cream fits under the lid. How many centimeters are in the minimum possible height of the ice cream in the cup? Express your answer to the nearest tenth. Question of the Day 2 (Calculators are permitted): What is the sum of the seven smallest composite numbers which cannot be determined to be composite simply by using the divisibility rules for 2, 3, 4, 5, 6, 8, 9, or 10? Question of the Day 3 (No calculators): What is the value of 1.000000000000 + 2.000000000000 + 3.000000000 + 4000000000 + 5.000000000000000? Previous Solution The lucky prime was 89. Note that I create the lucky prime before I see the answers you wrote. This is not biased in any way. The answer to yesterday's question was 225. No one got this question right. Solution to yesterday's question: The first step will be to find the prime factorization of 84 million. The prime factorization of 84,000,000 = 2^8 *3^1 * 5^6 * 7^1. Any number that is a factor of 84 million must have a prime factorization that uses the same prime factors raised to powers that do not exceed those from the prime factorization of 84 million. So a factor could have 2 as a prime factor with an exponent from 0 to 8, but because we want an ‘’even’’ factor, the number must be divisible by 2, meaning that the exponent of 2 cannot be 0. That gives us 8 choices (1 through 8) for the exponent. A factor of 84 million could have a 3 as a prime factor with 2 choices for the exponent (0 or 1). A factor of 84 million could have a 5 as a prime factor with 7 choices for the exponent (0 through 6). A factor of 84 million could have a 7 as a prime factor with 2 choices for the exponent (0 or 1). In total then, there are 8*2*7*2 = 224 numbers that would be an even factor of 84 million. Yes, Blueeighthnote. Prime numbers are already not divisible by 4 or 7. I might give hints that will not help you. Scoreboards 1. Blueeighthnote: 2365 points (2 achvmt pkgs) 2. TimBluesWin: 655 points (1 achvmt pkg) 3. Imamadmad: 645 points (1 achvmt pkg) 4. Julianthewiki: 420 points (1 achvmt pkg) 5. 69.235...: 230 points (1 achvmt pkg) 6. ZombieBird4000: 50 points (1 achvmt pkg) 7. Supermario3459: 45 points (1 achvmt pkg) 8. Wildoneshelper: 40 points (1 achvmt pkg) 9. Emmaelise401: 30 points 9. CalzoneManiac: 30 points 11. Googleaarex: 10 points (Here are 10 points to get you started!) Achievements Skills Badges! Usually awarded for having skills to solving hard questions, etc. 1. Quick Thinker! (+10 points) - Awarded for posting an answer before I write "Please leave your answers here." FIRST FOUNDED BY BLUEEIGHTHNOTE 2. RARE: Leaderboards Expert! (+300 points) - Awarded for being 1st place on the leaderboards for 30+ days. FIRST FOUNDED BY BLUEEIGHTHNOTE 3. RARE: More than a Millenium! (+100 points) - Awarded for being first in the leaderboards and scoring more than 1000 points from the runner-up. FIRST FOUNDED BY BLUEEIGHTHNOTE 4. Questions in a question (+20 points)? Awarded for finding three ambiguities in a single question. EARNED BY IMAMADMAD Earth Badges Most rare ones are found here. RARE: Top Ten (+30 points) - Awarded for being the first top 10 people ONLY to participate on the question of the day! EARNED BY THE FIRST 10 PARTICIPATING PEOPLE Sun Badges All epic ones are found here. Galaxy Badges Mysterious badges from a far-out universe. Each one found here is worth 10000+ points and/or 5+ achievement packages. Uniqueness Badges Unique things one can do in the answers section. ONLY ONE PERSON CAN EARN EACH BADGE. 1. Analyzer! (+10 points) - Awarded for drawing a diagram. FOUNDED BY IMAMADMAD 2. Inspiration! (+5 points) - A question was dedicated to you! FOUNDED BY BLUEEIGHTHNOTE Trustworthiness Badges Awarded by how much I trust someone on this wiki. Please do not ask me about these badges. 1. Reliability (+100 points) - Trusted to write a question of a day. FIRST FOUNDED BY BLUEEIGHTHNOTE, JULIANTHEWIKI, AND IMAMADMAD 2. Scoreboard Tinkerer (+100 points) - Trusted to change the scoreboards. FIRST FOUNDED BY BLUEEIGHTHNOTE AND JULIANTHEWIKI Duration Badges Yes! YOU KNOW IT! PARTICIPATION EVERY DAY! Category:Blog posts